Whakaoti i te x(x+3)/2-(x+1)^2/3+1/3=0

$$\frac { x ( x + 3 ) } { 2 } - \frac { ( x + 1 ) ^ { 2 } } { 3 } + \frac { 1 } { 3 } = 0$$

Whakaoti mō x

$$x=-5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3x\left(x+3\right)-2\left(x+1\right)^{2}+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x+3.

$$3x^{2}+9x-2\left(x+1\right)^{2}+2=0$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}+9x-2\left(x^{2}+2x+1\right)+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}+2x+1.

$$3x^{2}+9x-2x^{2}-4x-2+2=0$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}+9x-4x-2+2=0$$

Pahekotia te 9x me -4x, ka 5x.

$$x^{2}+5x-2+2=0$$

Tāpirihia te -2 ki te 2, ka 0.

$$x^{2}+5x=0$$

Tauwehea te x.

$$x\left(x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x+5=0.

$$x=0 x=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3x\left(x+3\right)-2\left(x+1\right)^{2}+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x+3.

$$3x^{2}+9x-2\left(x+1\right)^{2}+2=0$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}+9x-2\left(x^{2}+2x+1\right)+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}+2x+1.

$$3x^{2}+9x-2x^{2}-4x-2+2=0$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}+9x-4x-2+2=0$$

Pahekotia te 9x me -4x, ka 5x.

$$x^{2}+5x-2+2=0$$

Tāpirihia te -2 ki te 2, ka 0.

$$x^{2}+5x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}}}{2}$$

Tuhia te pūtakerua o te 5^{2}.

$$x=\frac{-5±5}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±5}{2} ina he tāpiri te ±. Tāpiri -5 ki te 5.

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-5±5}{2} ina he tango te ±. Tango 5 mai i -5.

$$x=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$x=-5$$

Kua oti te whārite te whakatau.

$$x=0 x=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3x\left(x+3\right)-2\left(x+1\right)^{2}+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x+3.

$$3x^{2}+9x-2\left(x+1\right)^{2}+2=0$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+1\right)^{2}.

$$3x^{2}+9x-2\left(x^{2}+2x+1\right)+2=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}+2x+1.

$$3x^{2}+9x-2x^{2}-4x-2+2=0$$

Pahekotia te 3x^{2} me -2x^{2}, ka x^{2}.

$$x^{2}+9x-4x-2+2=0$$

Pahekotia te 9x me -4x, ka 5x.

$$x^{2}+5x-2+2=0$$

Tāpirihia te -2 ki te 2, ka 0.

$$x^{2}+5x=0$$

Whakawehea te 5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{2}. Nā, tāpiria te pūrua o te \frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=\left(\frac{5}{2}\right)^{2}$$

Pūruatia \frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+5x+\frac{25}{4}=\frac{25}{4}$$

Tauwehea x^{2}+5x+\frac{25}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$x+\frac{5}{2}=\frac{5}{2} x+\frac{5}{2}=-\frac{5}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-5$$